Solve (1/2+2/5)div(3/4-1/5)=frac{3}{7}

$$( \frac{ 1 }{ 2 } + \frac{ 2 }{ 5 } ) \div ( \frac{ 3 }{ 4 } - \frac{ 1 }{ 5 } )= \frac{ 3 }{ 7 }$$

Verify

Solution Steps

Least common multiple of 2 and 5 is 10. Convert \frac{1}{2} and \frac{2}{5} to fractions with denominator 10.

$$\frac{\frac{5}{10}+\frac{4}{10}}{\frac{3}{4}-\frac{1}{5}}=\frac{3}{7}$$

Since \frac{5}{10} and \frac{4}{10} have the same denominator, add them by adding their numerators.

$$\frac{\frac{5+4}{10}}{\frac{3}{4}-\frac{1}{5}}=\frac{3}{7}$$

Add 5 and 4 to get 9.

$$\frac{\frac{9}{10}}{\frac{3}{4}-\frac{1}{5}}=\frac{3}{7}$$

Least common multiple of 4 and 5 is 20. Convert \frac{3}{4} and \frac{1}{5} to fractions with denominator 20.

$$\frac{\frac{9}{10}}{\frac{15}{20}-\frac{4}{20}}=\frac{3}{7}$$

Since \frac{15}{20} and \frac{4}{20} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{9}{10}}{\frac{15-4}{20}}=\frac{3}{7}$$

Subtract 4 from 15 to get 11.

$$\frac{\frac{9}{10}}{\frac{11}{20}}=\frac{3}{7}$$

Divide \frac{9}{10} by \frac{11}{20} by multiplying \frac{9}{10} by the reciprocal of \frac{11}{20}.

$$\frac{9}{10}\times \frac{20}{11}=\frac{3}{7}$$

Multiply \frac{9}{10} times \frac{20}{11} by multiplying numerator times numerator and denominator times denominator.

$$\frac{9\times 20}{10\times 11}=\frac{3}{7}$$

Do the multiplications in the fraction \frac{9\times 20}{10\times 11}.

$$\frac{180}{110}=\frac{3}{7}$$

Reduce the fraction \frac{180}{110} to lowest terms by extracting and canceling out 10.

$$\frac{18}{11}=\frac{3}{7}$$

Least common multiple of 11 and 7 is 77. Convert \frac{18}{11} and \frac{3}{7} to fractions with denominator 77.

$$\frac{126}{77}=\frac{33}{77}$$

Compare \frac{126}{77} and \frac{33}{77}.

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